Question 924137
P(6,-2),M(0,5),Q(x2,y2)


Since formula for midpoint is:
{{{(x1 + x2) / 2}}} and {{{(y1 + y2) / 2}}}

Then formula for {{{x2}}} and {{{y2}}} is:
{{{x2 = 2(Mx) - x1}}}
{{{y2 = 2(My) - y1}}}

where {{{Mx}}} is the {{{x}}} coordinate of the {{{midpoint}}}, and {{{My}}} the {{{y}}} coordinate of the {{{midpoint}}}

so, we have:

{{{x2 = 2(Mx) - x1}}}
{{{x2 = 2(0) - 6}}}
{{{x2 = 0 - 6}}}
{{{x2 = -6}}}

{{{y2 = 2(My) - y1}}}
{{{y2 = 2(5) - (-2)}}}
{{{y2 = 10 +2}}}
{{{y2 =12}}}

so, Q(x2,y2)=Q(-6,12)

Checking:
{{{M = (x1 + x2) / 2}}} and {{{(y1 + y2) / 2}}}
{{{M = (6 +(-6)) / 2}}} and {{{(-2 + 12) / 2}}}
{{{M = (6-6) / 2}}} and {{{(-2 + 12) / 2}}}
{{{M = 0/ 2}}} and {{{10 / 2}}} 
{{{M}}} = {{{0}}}, {{{5}}}

We got the right midpoint.

Thus, the coordinates of Q are ({{{-6}}},{{{ 12}}})